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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Sun, 21 Jul 2024 15:57:17 -0700
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On 7/21/2024 3:56 PM, Chris M. Thomasson wrote:
> On 7/10/2024 2:30 PM, Chris M. Thomasson wrote:
>> On 7/9/2024 3:16 PM, Moebius wrote:
>>> Am 09.07.2024 um 22:27 schrieb sobriquet:
>>>
>>>> How do you define sets exactly?
>>>
>>> Actually, we don't _define_ the concept of /set/ by a "proper 
>>> definition".
>>>
>>>> Is there a specific set that corresponds to sqrt(2)?
>>>
>>> Well, rather a sequence (which is a certain kind of set in the 
>>> context of set theory):
>>>
>>> (1, 1.4, 1.41, 1.414, ...)
>>>
>>>> Does this set have an infinite number of elements analogous to the 
>>>> sqrt(2) having an infinite decimal expansion?
>>>
>>> Yes. See above. This sequence (called an /infinite sequence/) has 
>>> infinitely many terms.
>>>
>>>> It seems that the existence of something like sqrt(2) is already 
>>>> rather dubious.
>>>
>>> Oh, really?
>>>
>>> If you say so.
>>>
>>> So in your "math" there is no /number/ x such that x^2 = 2.
>>>
>>> Ok, if you can live with(out) that, fine.
>>>
>>>> In reality, things are finite and space and time might also be 
>>>> finite (composed of atoms of space and time that can't be subdivided 
>>>> with
>>>> the parts retaining their original spatial and temporal properties).
>>>
>>> Yes, they could.
>>>
>>>> So if the concept of irrational numbers like sqrt(2) [etc.]
>>>
>>> Hint (1): You won't find numbers like sqrt(2) IN (PHYSICAL) REALITY.
>>
>> If we draw a unit square, sqrt 2 is in there by default, right? From 
>> the unit square all other squares can be constructed.
>>
>>
>>
>>>
>>> Hint (2): You won't find numbers like 1, 2, 3 there neither/either (?).
>>>
>>>
>>
> 
> Also, from the unit circle, all circles and ellipses can be created. The 
> ellipse aspect is that of a circle rotated in 3d is an ellipse when 
> viewed on the projected plane. Check this out in VR:
> 
> https://skfb.ly/6RozT

Think of a circle in 3d. Looking at it dead on as a circle. Then, change 
the camera view. It becomes an ellipse.